Visual Quantum Mechanics

Prepared for Contemporary Physics by Dean Zollman, Wally Axmann, Bob Grabhorn, Carol Regehr, and Paul Donovan Spring, 1994
From Kansas State University:http://bluegiant.phys.ksu.edu/dvi/vqm/vqm.html

5. Potential and Kinetic Energy Diagrams --Large Objects

When we work with Newton's Laws, we frequently write down the forces acting on an object. Then, we use the forces to predict how the object will behave at any future time. However, we could equally well develop ideas of motion by starting with energy as the fundamental idea. In situations that we encounter while studying quantum concepts, we generally find energy the easier concept to use.

As an example of using energy to describe motion, consider a small cart moving on a level, very low-friction surface. If we ignore the friction entirely, then the cart always has whatever energy it had at the beginning of its motion. No potential energy exists in this case, so the total energy is equal to the kinetic energy; the potential energy is zero. A simple graph or diagram describes this situation:

In a real situation, even on an air track, the cart does not go on forever. Instead, it strikes the end of the track and turns around. With a perfect collision at the end of the track, the cart would have the same kinetic energy before and after the collision with the end; only the direction would change. However, during the collision the cart's speed decreases to zero. Plotting kinetic energy versus distance, we get another diagram.

Looking at the end of the track, we see what happens during the collision. The flexible steel springs on the cart and track bend. This process increases the elastic potential energy, resulting in a different diagram

We can combine kinetic, potential, and total energies for this situation into a single diagram

Consider the question: For each value of kinetic energy, how far will the metal on the ends compress? The first step in our answer is to draw the potential energy diagram for the situation. It looks like the first of the three diagrams above. The high sides indicate that the potential energy gets very large at the ends of the track. Now pick a value for kinetic energy. What is the furthest location to the left that the cart will reach? Why?

Now we add a magnet at the center of the track and on the cart so that the magnets attract. Look at the kinetic energy diagram for the cart:

The total energy does not change, so the potential energy must be as shown here:

For most situations, we can draw a potential energy diagram by following similar reasoning patterns.

Visual Quantum Mechanics: Table of Contents